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# Does Size Affect How a Ball Travels?

by
Matthew Lee
Matthew Lee has been writing professionally since 2007. Past and current research projects have explored the effect of a diagnosis of breast cancer on lifestyle and mental health and adherence to lifestyle-based (i.e. nutrition and exercise) and drug therapy treatment programs. He holds a Master of Arts in psychology from Carleton University and is working toward his doctorate in health psychology.
Friends are playing with a ball on the beach. Photo Credit Medioimages/Photodisc/Photodisc/Getty Images

Whether on the ground or in the air, a variety of forces contribute to the motion of a ball. Focusing on spherical balls -- such as those used in golf, baseball and basketball -- their size and mass help determine how they travel. In addition to having an impact on speed and trajectory, the size and mass of balls also contribute to how external forces affect them. When two balls of the same diameter are made of materials of different density and mass, the ball with the greater mass-density will travel farther if projected with the same amount of force, or at the same initial speed.

## Mass-Density

Physics refers to balls such as those used in competitive sports as "rigid bodies." For rigid bodies in motion, the principles of the physics field called "dynamic" apply. Among the factors that help to determine how a rigid body moves, its mass per unit length, or mass-density, plays a vital role both on the ground and in the air. An object with high mass-density proves more difficult to move and also more difficult to stop once it begins moving.

## Objects in Flight

The difference between softballs and the shots used in shot putting provide a great example of the effects of mass-density. Although both are approximately equal in diameter, you'll find the mass of the heavy metal shot much higher than that of the softball. As such, shot putting requires a greater amount of strength, or initial force, than throwing a softball. Due to the shot's high mass-density, however, forces such as air friction and the downward pull of gravity affect its flight less than a softball's. In other words, the shot will travel farther than the softball, because its mass makes it less vulnerable to air friction and gravity.

## Objects on the Ground

While the law of inertia works in a similar fashion on both the air and the ground, the forces that help to determine how a ball rolls differ slightly between the two. On level ground, gravity and air friction do not factor significantly into how an object rolls. In place of the forces of gravity and air friction, surface friction plays a major role in determining how balls roll. Similar to balls in flight, surface friction impedes the movement of balls with low mass-density, such as soccer balls, more than it does those with high mass-density, such as bowling balls. In other words, given equal size in terms of diameter, the ball with the greater mass will roll farther.

## Initial Force and Motion

Due to the different effects of external forces, balls with high mass-density would travel farther and faster than those with low mass-density if you could launch both with an infinite amount of force. Although you can't do this, throwing or rolling balls of different mass-densities at the same initial speed obtains the same effect. Hitting a golf ball with more power than a ping pong ball provides illustration. When you launch both at the same initial speed, the golf ball is sent soaring, while air friction ends the ping pong ball's flight shortly after it leaves the tee.

You can see similar effects on the ground. While it would require a greater amount of force to roll both at the same initial speed, a bowling ball's higher mass-density would give it greater rotational momentum than a rolled basketball. Surface would soon slow the basketball down, eventually stopping it while the high mass-density and rotational force of the bowling ball will continue to carry it for a longer distance.

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